What I did when I started out (and still do now) is simply watch TV with my bass in hand. Whenever ANY kind of bass line comes up during a show or commercial or whatever, I listen to it and try to play it. Doing this forces me to focus on the music more than usual, since I know I only have a limited time to learn the song before the commercial ends or TV show changes scenes. It also gets me exposed to different types of music, as well as things I know I would probably never listen to or learn about otherwise.
One of my favorite things to do is wait until nighttime and then listen to the bands that play on all the nighttime talk shows and comedy shows (Jay Leno, SNL, etc.). I try to play along with the bands, and learn their bass lines.
If there's a particular song or composition that I want to learn (such as if I'm transcribing a walking bass line from a jazz tune), I listen to that particular song for days and days on end. I even listen to it constantly when I sleep. I do this until the song is stuck in my head, and I can play the song's entire bass line in my head with no trouble. From there, I translate that memory into singing; that is, I sing the bassline before actually playing it. Then, I translate the singing to the bass.
